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Sino-German Workshop on Electromagnetic Processing of Materials,
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Transcript of Sino-German Workshop on Electromagnetic Processing of Materials,
Sino-German Workshop on Electromagnetic Processing of Materials,11.10 – 13.10.2004 Shanghai, PR China
Magnetic Field Control of Heat and Mass Transport Processes in Industrial Growth of Silicon and III-V
Semiconductors Crystals
J.Dagner, P. Schwesig, D. Vizman, O. Gräbner, M.Hainke, J.Friedrich, G.Müller
Outline:• Time dependent magnetic fields applied to growth process of InP
• Stationary magnetic fields in large scale Czochralski facilities
Process: Vertical Gradient Freeze (VGF) growth of InP
Task: Substrates with low dislocation density without additional dopands for lattice hardening
Problem: Generation of dislocations during the relaxation of thermal stresses
Possible Solution: Usage of time dependent magnetic fields to control convective heat transferèChange the shape of the solid liquid interface in order to minimize the von Mises StressèOptimization using numerical modeling
Motivation Motivation
Melt
Crystal
Crucible
Numerical modeling Numerical modeling Furnace Setup : • Existing VGF setup located at the
Crystal Growth Laboratory in Erlangen (currently used for R&D activities for S-doped InP)
• Already optimized thermal field using numerical modeling
Numerical Modeling:• Global model of the complete setup
for heat transfer with CrysVUn (conduction radiation and melt convection)
• Quasistationary calculations for different position of the phase boundary
• Investigated field types:Rotating magnetic fields (RMF)Traveling magnetic fields (TMF)
Insulation
Inert gas
9 Heating zones
Crucible support
Steel autoclave
Boron-oxide Melt cover
InP Crystal
No significant influence on the bending of the interface and the resulting von Mises stress
Process time
Applying RMF to the standard growth processApplying RMF to the standard growth process
Bending (b) of the solid liquid interface for different process times.
Max. von Mises stress at solid liquid interface for different process times.
Melt
Crystal
concave convex
b>0b<0
Interface
Upward configuration
Downward configuration
Standard Process
1,2 MPa
2,0 mm
4,6 mm/s
2,1 MPa0,6 MPaMax. von Mises stress at the phase boundary
2,1 mm1,6 mmBending of the solid liquid interface
9,6 mm/s5,3 mm/sMaximum velocity in the melt. Only the down-
ward configuration is useful
Applying TMF to the standard growth process – Applying TMF to the standard growth process – influence of the orientation of the Lorentz-forceinfluence of the orientation of the Lorentz-force
Aspect ration: 0.5
IsothermsdT = 1k
Streamlines
• Function of the velocity in z direction has a minimum• The bending of the solid liquid interface changes from concave to concave-
convex shape (hat or W-shape)
Applying TMF – Influence of the strength of the Applying TMF – Influence of the strength of the magnetic induction on the flow pattern magnetic induction on the flow pattern
Streamlines for different magnetic induction at a aspect ration of 0.9. Only half of the computational domain is show.
è Minimum of the von Mises stress at 5,5 mT, but the phase boundary has a W-shape.
è Two contradicting optimization criteria:a) Minimization of the bending of the phase boundaryb) Minimization of von Mises stress at the phase boundary
PG.max
PG.max PG
.max
MPaPG 93,0.max MPaPG 57,0.max MPaPG 33,0.max
Applying TMF – Resulting von Mises stress at the solid Applying TMF – Resulting von Mises stress at the solid liquid interface liquid interface
Comparison of the results for RMF and TMFComparison of the results for RMF and TMF
Rotating magnetic fields (RMF):
• Only small influence on the bending of the phase boundary and the resulting von Mises stress(< 15%)
• Higher growth velocities have no advantages, in contrast to prior studies on GaAs (Hainke et al. Magnethydrodynamics 39:513-519 2003)
Traveling magnetic fields (TMF):
• Reduction of the resulting von Mises stress while maintaining a flat phase boundary
• Further reduction is possible if a W-shape interface does not create additional problems in the growth process• Major drawback for the practical application: The integration of an inductor for
generating a TMF in a high pressure and high temperature vessel with corrosive atmosphere (Phosphor vapor) is complicated and expensive.
(Schwesig et al. Journal of Crystal Growth 226:224-228 2004)
Conclusions –Part IConclusions –Part I
transversal axial cusp
Czochralski growth of Si crystalsCzochralski growth of Si crystals
Objectives for using magnetic fields: • Stabilization of convection • Reduction of temperature fluctuations• Control of oxygen transport and interface shape
Field strength:• several mT up to several hundreds of mT
Optimization of the seeding phase by reducing Optimization of the seeding phase by reducing diameter fluctuations diameter fluctuations
Magnetic field
with without
Magnetic field
with
without
Magnetic field
with
without
Hirmke, Study Work 2001
Dia
met
erTe
mpe
ratu
re 5K
1mm
Time in sec
(in collaboration with Siltronic)
Czochralski growth of Si crystals under the influence of Czochralski growth of Si crystals under the influence of steady magnetic fieldssteady magnetic fields
Determination of the temperature distribution in the melt and at the crucible wall by using a special thermocouple set-up
Gräbner, Proc. EMRS 2000
Measured temperature distribution at the wall (lines) compared with calculated values (point).
x = -20rpm, c = 2rpm
x = -20rpm, c = 5rpm
Experiment 2D - Simulation
Axial Field 128mTx = -20rpm, c = 5rpm
Cusp Field 40mTx = -20rpm, c = 5rpm
Experiment 2D - Simulation
Czochralski growth of Si crystals under the influence of Czochralski growth of Si crystals under the influence of steady magnetic fieldssteady magnetic fields
Temperature distribution in a Si melt with 20kg under different process conditions – stationary numerical simulations with fixed shape of the melt pool; low Reynolds number k- model (CFD-ACE); magnetic fields by FZHDM1.
[1] Mühlbauer et. al. J.o.Cryst.Growth 1999 pp 107
3D view
Crystal rotation: x = -15rpmCrucible rotation: c = 4rpm
Side view
300mm
Czochralski growth of Si crystals under the influence of Czochralski growth of Si crystals under the influence of steady magnetic fieldssteady magnetic fields
Shape of solid/liquid interface under the influence of a horizontal magnetic field. Calculations (magnetic and flow field) with STHAMAS 3D. Free melt surface. The temperature is color-coded.
Vizman, PAMIR 2002
Static magnetic fields:• Widely used for large scale Czochralski process• Measurement techniques for obtaining temperature values in the melt
are available• Comparing this measured data to values obtained by numerical
simulations show a qualitative agreement• Simulation of Czochralski process is still a matter of intense research
Conclusions –Part IIConclusions –Part II
Acknowledgement Acknowledgement
This work is financially supported by the German federal ministry of education and research and Humbolt foundation.
The calculations with CFD-ACE were performed at SILTRONIC, Burghausen, Germany